DOI QR코드

DOI QR Code

A damage model predicting moderate temperature and size effects on concrete in compression

  • Hassine, Wiem Ben (Universite de Tunis El Manar, Ecole Nationale d'Ingenieurs de Tunis, Laboratoire de Genie Civil) ;
  • Loukil, Marwa (Universite de Tunis El Manar, Ecole Nationale d'Ingenieurs de Tunis, Laboratoire de Genie Civil) ;
  • Limam, Oualid (Universite de Tunis El Manar, Ecole Nationale d'Ingenieurs de Tunis, Laboratoire de Genie Civil)
  • 투고 : 2019.02.01
  • 심사 : 2019.04.09
  • 발행 : 2019.05.25

초록

Experimental isotherm compressive tests show that concrete behaviour is dependent on temperature. The aim of such tests is to reproduce how concrete will behave under environmental changes within a moderate range of temperature. In this paper, a novel constitutive elastic damage behaviour law is proposed based on a free energy with an apparent damage depending on temperature. The proposed constitutive behaviour leads to classical theory of thermo-elasticity at small strains. Fixed elastic mechanical characteristics and fixed evolution law of damage independent of temperature and the material volume element size are considered. This approach is applied to compressive tests. The model predicts compressive strength and secant modulus of elasticity decrease as temperature increases. A power scaling law is assumed for specific entropy as function of the specimen size which leads to a volume size effect on the stress-strain compressive behaviour. The proposed model reproduces theoretical and experimental results from literature for tempertaures ranging between $20^{\circ}C$ and $70^{\circ}C$. The effect of the difference in the coefficient of thermal expansion between the mortar and coarse aggregates is also considered which gives a better agreement with FIB recommendations. It is shown that this effect is of a second order in the considered moderate range of temperature.

키워드

참고문헌

  1. Abdulhaleem, K.N., Gulsan, M.E. and C evik, A. (2018), "Mechanical behavior of steel fiber-reinforced self- compacting concrete corbels at elevated temperatures", Struct. Concrete, 19(2), 1-14. https://doi.org/10.1002/suco.201700034.
  2. Ashteyat, A.M. and Ismeik, M. (2018), "Predicting residual compressive strength of self-compacted concrete under various temperatures and relative humidity conditions by artificial neural networks", Comput. Concrete, 21(1), 47-54. DOI: 10.12989/cac.2018.21.1.047.
  3. Basaran, C. and Nie, S. (2004), "An irreversible thermodynamics theory for damage mechanics of solids", Int. J. Damage Mech., 13(3), 205-223. https://doi.org/10.1177/1056789504041058.
  4. Bazant, P.Z. and Jirasek, M. (2002), "Non local integral formulations of plasticity and damage: Survey and progress", J. Eng. Mech., 128(11), 1119-1149. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119).
  5. Bazant, Z.P. and Xiang, Y. (1997), "Size effect in compression fracture: splitting crack band propagation", J. Eng. Mech., 123(2), 162-172. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:2(162).
  6. Carpinteri, A., Chiaia, B. and Ferro, G. (1995), "Size effects on nominal tensile strength of concrete structures: multifractality of material ligaments and dimensional transition from order to disorder", Mater. Struct., 28, 311-317. https://doi.org/10.1007/BF02473145
  7. Del Viso, J.R., Carmoa, J.R. and Ruiz, G. (2008), "Shape and size effects on the compressive strength of high strength concrete", Cement Concrete Res., 38, 386-395. https://doi.org/10.1016/j.cemconres.2007.09.020.
  8. Eren Gulsan, M., Abdulhaleem, K.N., Kurtoglu, A.E. and Cevik, A. (2018), "Size effect on strength of Fiber-Reinforced Self-Compacting concrete (SCC) after exposure to high temperatures", Comput. Concrete, 21(6), 681-695. https://doi.org/10.12989/cac.2018.21.6.681.
  9. Ju, J.W. (1989), "On energy based coupled elastoplastic damage theories: Constitutive modeling and computational aspects", Int. J. Solid. Struct., 25(7), 803-833. https://doi.org/10.1016/0020-7683(89)90015-2.
  10. Kachanov, L. (1958), "Time of the rupture process under creep conditions", Izvestiia Akademii Nauk SSSR, Otdelenie Teckhnich-eskikh Nauk, 8, 26-31.
  11. Kale, S. and Ostoja- Starzewski, M. (2017), "Representing stochastic damage evolution in disordered media as a jump Markov process using the fiber bundle model", Int. J. Damage Mech., 26(1), 147-161. https://doi.org/10.1177/1056789516650249.
  12. Kallel, H., Carre, H., Laborderie, C., Masson, B. and Tran, N.C. (2018), "Evolution of mechanical properties of concrete with temperature and humidity at high temperatures", Cement Concrete Compos., 91, 59-66. https://doi.org/10.1016/j.cemconcomp.2018.04.014.
  13. Lemaitre, J. and Chaboche, J. (1978), "Aspects phenomenologiques de la rupture par endommagement", J. Mecanique Appliquee, 2(3), 317-365.
  14. Liang, J.F., Yang, Z., Yi, P.H. andWang, J.B. (2017), "Stress-strain relationship for recycled aggregate concrete after exposure to elevated temperatures", Comput. Concrete, 19(6), 609-615. https://doi.org/10.12989/cac.2017.19.6.609.
  15. Limam, O., Aidi, M. and Zenzri, H. (2014), "Structural nominal concrete strength derived by statistical mechanics", Physica A, Statist. Mech. Appl., 395, 48-57. https://doi.org/10.1016/j.physa.2013.10.046.
  16. Masad, N. (2013), "Meso scale model for simulations of concrete subjected to cryogenic temperatures", PhD Thesis, Texas University.
  17. Mazars, J. (1986), "A description of micro and macroscale damage of concrete structures", Eng. Fract. Mech., 25(5-6), 729-737. https://doi.org/10.1016/0013-7944(86)90036-6.
  18. Mazars, J., Pijaudier-Cabot, G. and Saouridis, C. (1991), "Size effect and continuous damage in cementitious materials", Int. J. Fract., 51,159-173. https://doi.org/10.1007/BF00033976.
  19. Miled, K., Limam, O. and Sab, K. (2012), "A probabilistic mechanical model for prediction of aggregates' size distribution effect on concrete compressive strength", Physica A, Statist. Mech. Appl., 391, 3366-3378. https://doi.org/10.1016/j.physa.2012.01.051.
  20. Miura, T. (1989), "The properties of concrete at very low temperatures", Mater. Struct., 22, 243-254. https://doi.org/10.1007/BF02472556.
  21. Muller, H., Anders, I., Breiner, R. and Vogel, M. (2013), "Concrete: treatment of types and properties in fib model code 2010", Struct. Concrete, 14(4), 320-334. https://doi.org/10.1002/suco.201200048.
  22. Nandan, H. and Singh, M.P. (2014), "Effects of thermal environment on structural frequencies, Part I A simulation study", Eng. Struct., 81, 480-490. https://doi.org/10.1016/j.engstruct.2014.06.046.
  23. Nemat Nasser, S. and Horii, H. (1982), "Compression induced non planar crack extension with application to splitting", J. Geophys. Res., 87, 6805-6821. https://doi.org/10.1029/JB087iB08p06805.
  24. Ostoja-Starzewski, M. (1998), "Damage in a random microstructure: Size effects, fractals, and entropy maximization", Appl. Mech. Rev., 42(11), 202-212. doi:10.1115/1.3152391.
  25. Pijaudier-Cabot, G. and Bazant, Z.P. (1987), "Non local damage theory", J. Eng. Mech., 113, 1512-1533. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1512).
  26. Rinaldi, A. and Mastilovic, S. (2014), "The Krajcinovic approach to model size dependent fracture in quasi brittle solids", Mech. Mater., 71, 21-33. https://doi.org/10.1016/j.mechmat.2014.01.005.
  27. Shoukry, S.N., William, G.W., Downie, B. and Riad, M.Y. (2011), "Effect of moisture and temperature on the mechanical properties of concrete", Constr. Build. Mater., 25, 688-696. https://doi.org/10.1016/j.conbuildmat.2010.07.020.
  28. Pijaudier-Cabot, G., Reynouard, J.M. and Torrenti, J.M. (2013), Mechanical Behavior of Concrete, ISTE and Wiley.
  29. Tsallis, C. (2009), "Computational applications of non-extensive statistical mechanics", J. Comput. Appl. Math., 227, 51-58. https://doi.org/10.1016/j.cam.2008.07.030.
  30. Vu, C.C., Weiss, J., Ple, O., Amitranoand, D. and Vandembroucq, D. (2018), "Revisiting statistical size effects on compressive failure of heterogeneous materials, with a special focus on concrete", J. Mech. Phys. Solid., 121, 47-70. https://doi.org/10.1016/j.jmps.2018.07.022.
  31. Wang, H., Tan, G., Wang, W. and Liu, Z. (2018), "Effect of temperature and spring-mass systems on modal properties of Timoshenko concrete beam", Struct. Eng. Mech., 65(4), 389-400. https://doi.org/10.12989/sem.2018.65.4.389.
  32. Yu, T.Q., Miao, X.S., Xiong, J.M., Jiang, H. and Lee, H. (1989), "An orthotropic damage model for concrete at different temperatures", Eng. Fract. Mech., 32(5), 715-786. https://doi.org/10.1016/0013-7944(89)90174-4.

피인용 문헌

  1. Flexural strength of concrete-galvalume composite beam under elevated temperatures vol.27, pp.1, 2019, https://doi.org/10.12989/cac.2021.27.1.013